In astrophysics, the virial mass is the mass of a gravitationally bound astrophysical system, assuming the virial theorem applies. In the context of galaxy formation and dark matter halos, the virial mass is defined as the mass enclosed within the virial radius of a gravitationally bound system, a radius within which the system obeys the virial theorem. The virial radius is determined using a "top-hat" model. A spherical "top hat" density perturbation destined to become a galaxy begins to expand, but the expansion is halted and reversed due to the mass collapsing under gravity until the sphere reaches equilibrium – it is said to be virialized. Within this radius, the sphere obeys the virial theorem which says that the average kinetic energy is equal to minus one half times the average potential energy, , and this radius defines the virial radius. Virial radius The virial radius of a gravitationally bound astrophysical system is the radius within which the virial theorem applies. It is defined as the radius at which the density is equal to the critical density of the Universe at the redshift of the system, multiplied by an overdensity constant : where is the halo's mean density within that radius, is a parameter, is the critical density of the Universe, is the Hubble parameter, and is the virial radius. The time dependence of the Hubble parameter indicates that the redshift of the system is important, as the Hubble parameter changes with time: today's Hubble parameter, referred to as the Hubble constant , is not the same as the Hubble parameter at an earlier time in the Universe's history, or in other words, at a different redshift. The overdensity is given by where , and . Since it depends on the density parameter , its value depends on the cosmological model used. In an Einstein–de Sitter model it equals . This definition is not universal, however, as the exact value of depends on the cosmology. In an Einstein–de Sitter model, it is assumed that the density parameter is due to matter only, where . Compare this to the currently accepted cosmological model for the Universe, ΛCDM model, where and ; in this case, (at a redshift of zero; the value approaches the Einstein-de Sitter value with increased redshift). Nevertheless, it is typically assumed that for the purpose of using a common definition, and this is denoted as for the virial